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Old 2016-09-26, 10:04   #5
Raman
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"Mr. Tuch"
Dec 2007
Chennai, India

3·419 Posts
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I had to add up on with in a some of these prime factors for in to factordb.com web site page - for only of certainly ≤ 10000000 digits - limit range bound level - rate ratio scale proportion - exists out!
Factordb.com web site page does not accept with in a some of larger factors for ≥ 10000000 digits - exists out - for only of certainly!
Factordb.com web site page 10000000 digit limit exists out - parallel execution queries limit exists out - sequential input queries limit exists out!
Factordb.com web site page does not mark out larger known found out prime numbers and then or probable prime numbers called as out - known as out!
Been got out - seeking out - looking out - obtaining out - attaining out!

With in this following PARI/GP command only certainly and then or script
you could be able on to getting away with the very much all most all prime factors of 2p-1 and then or (2p+1)/3 both simultaneously - a some - of just the following given fixed form!
And then or - called as out - known as out - namely - that which it that!
p = (279+1)/3
Code:
p=(2^79+1)/3
forstep(q=2*p+1,10^50,2*p,if(Mod(4,q)^p==1,print(q)))
Of for of for - with in only certainly - away up out down off my own - that ever which ever a way a way ever - by using be being that way - that which it that. And then or - and then or - of for from front frontier - right now that by right now that itself at this very moment variably. Very much all most all - away up out down off my own - that ever which ever a way a way ever - by using be being that way - that which it that. Once written out - one single time - time period frame duration - time times know known. A some - a some - a some - a some - a some - a some - a some - very much all most all. Away up out down off my own - that ever which ever a way a way ever - by using be being that way - that which it that. Once written out - one single time - time period frame duration - time times know known. Called as out - known as out! Once written out - one single time - time period frame duration - time times know known. And then or. Namely - that which it that. A some - a some - a some - a some - a some - a some - a some - very much all most all. Just an other point always - called as out - known as out - a some - very much all most all. A some - limit range bound level - rate ratio scale proportion - exists out - very much all most all!
Right now that I am trying it out ECM curves up on over at following four numbers (28191+1)/3, (219937+1)/3, (2110503+1)/3, (2524287+1)/3 with in higher bounds on a four core micro processor.

Double Mersenne
Code:
23-1 is prime.
27-1 is prime.
231-1 is prime.
2127-1 is prime.
28191-1 has the factors: 338193759479, 210206826754181103207028761697008013415622289.
2131071-1 has the factors: 231733529, 64296354767.
2524287-1 has the factors: 62914441, 5746991873407, 2106734551102073202633922471, 824271579602877114508714150039, 65997004087015989956123720407169.
22147483647-1 has the factors: 295257526626031, 87054709261955177, 242557615644693265201, 178021379228511215367151.
Wagstaff Mersenne
Code:
(23+1)/3 is prime.
(27+1)/3 is prime.
(231+1)/3 is prime.
(2127+1)/3 is prime.
(28191+1)/3 is composite.
(2131071+1)/3 has a factor: 2883563.
(2524287+1)/3 is composite.
(22305843009213693951+1)/3 has a factor: 1328165573307087715777.
If the new Mersenne conjecture of of just that is being true, and then or 22305843009213693951-1 - is being that - should be that - a some composite number - indeed obviously rather than instead of!
What is being the probability and then or likelihood that at least one of the four numbers, namely - that which it that - 22305843009213693951-1, then, 2618970019642690137449562111-1, or, 2162259276829213363391578010288127-1, and, 2170141183460469231731687303715884105727-1, - could be that - must be that - ought on to be that - a some prime number?
Once written out - one single time - time period frame duration - time times know known
Namely - that which it that

If the new Mersenne conjecture of of just that is being true, and then or (22147483647+1)/3 - is being that - should be that - a some composite number - indeed obviously rather than instead of!
If the new Mersenne conjecture of of just that is being true, and then or 2768614336404564651-1 - is being that - should be that - a some composite number - indeed obviously rather than instead of!

What is being the probability and then or likelihood that at least one of the four numbers, namely - that which it that - (22147483647+1)/3, then, (2618970019642690137449562111+1)/3, or, (2162259276829213363391578010288127+1)/3, and, (2170141183460469231731687303715884105727+1)/3, - could be that - must be that - ought on to be that - a some prime number?
What is being the probability and then or likelihood that at least one of the four numbers, namely - that which it that - 256713727820156410577229101238628035243-1, then, (256713727820156410577229101238628035243+1)/3, or, 2170141183460469231731687303715884105727-1, and, (2170141183460469231731687303715884105727+1)/3, - could be that - must be that - ought on to be that - a some prime number?
What is being the probability and then or likelihood that at least one of the four numbers, namely - that which it that - 2715827883-1, then, 22932031007403-1, or, 2768614336404564651-1, and, 2845100400152152934331135470251-1, - could be that - must be that - ought on to be that - a some prime number?
What is being the probability and then or likelihood that at least one of the four numbers, namely - that which it that - (2715827883+1)/3, then, (22932031007403+1)/3, or, (2845100400152152934331135470251+1)/3, and, (256713727820156410577229101238628035243+1)/3, - could be that - must be that - ought on to be that - a some prime number?

Mersenne Wagstaff
Code:
23-1 is prime.
211-1 = 23 × 89.
243-1 = 431 × 9719 × 2099863.
2683-1 = 1367 × 434836499112609694795723958417048861299768144283442662402095922180462812746769 × 67513796971703570854592232797421324116119881147340327278928245456644619398078155616494185719845536064262986241999463764460809.
22731-1 has the factors: 93968249, 5235895818143, 697275709026751, 563358792984278565516774152727223543227673.
243691-1 has the factors: 87383, 1398113, 4690767254460090160943, 1787363373488812416764791.
2174763-1 is composite.
22796203-1 has the factors: 5592407, 17017419583182311, 23349981773942355169801.
2201487636602438195784363-1 has a factor: 14549422239062062117588852231.
Double Wagstaff
Code:
(23+1)/3 is prime.
(211+1)/3 is prime.
(243+1)/3 is prime.
(2683+1)/3 = 1676083 × 26955961001 × 296084343545863760516699753733387652635366098889116410731661924253563729059085336779932810899819313612925255002666691226800507277398580985624625950496168983999760414855301693388419156899841.
(22731+1)/3 has the factors: 67399191280564009798331, 2252735939855296339250682011.
(243691+1)/3 has a factor: 349529.
(2174763+1)/3 has a factor: 173085275201.
(22796203+1)/3 has a factor: 129469791307.
(2768614336404564651+1)/3 has a factor: 3290547117383710719111443.
(2201487636602438195784363+1)/3 has the factors: 183756724581423634555339057, 101874969893105185923314913883.
Mersenne Fermat
Code:
23-1 is prime.
25-1 is prime.
217-1 is prime.
2257-1 = 535006138814359 × 1155685395246619182673033 × 374550598501810936581776630096313181393.
265537-1 has the factors: 513668017883326358119, 883852340565787164089923172087.
Wagstaff Fermat
Code:
(23+1)/3 is prime.
(25+1)/3 is prime.
(217+1)/3 is prime.
(2257+1)/3 = 37239639534523 × 518144156602508243009 × 4000659204579114753312310878847043394855313.
(265537+1)/3 has a factor: 13091975735977.
Code:
Larger candidate numbers - fewer prime factors - pumped out - not - not - smaller - not - not - several - very much all most all - a some - and prime then composite or unique! Shorter candidate numbers - many prime factors - pumped out - not - not - bigger - not - not - lesser - very much all most all - a some - and prime then composite or unique! Cunningham Tables numbers candidates! Fibonacci numbers, Lucas Numbers, Homogeneous Cunningham Numbers and other twisted additive or multiplicative groups like these things. As ≠ like last final ultimate next previous letter character alphabet digit number numeral cardinal ordinal stuff.
As ≠ like last final ultimate next previous letter character alphabet digit number numeral cardinal ordinal stuff. Fibonacci numbers, Lucas Numbers, Homogeneous Cunningham Numbers and other twisted additive or multiplicative groups like these things. Cunningham Tables numbers candidates! Lower candidate numbers - a lot of prime factors - pumped out - not - not - greater - not - not - sparser - very much all most all - a some - and prime then composite or unique! Huger candidate numbers - rarer prime factors - pumped out - not - not - tinier - not - not - a plenty of - very much all most all - a some - and prime then composite or unique!

Last fiddled with by Raman on 2016-09-26 at 10:35 Reason: Wrapped code tags to keep width of window in check.
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